Q: Does every rational number have an additive inverse and why?

Write your answer...

Submit

Still have questions?

Continue Learning about Basic Math

Yes.

That would be the set of all non-zero numbers. If by number you actually meant whole numbers, that is integers, then it would be the set of all non-zero integers. They are also called Additive Inverses. For example, -5 is the additive inverse of 5, because 5 + (-5) = 0. Similarly, 7 is the additive inverse of -7 because (-7) + 7 = 0.

Every positive rational number and its negative are the two square roots of the same positive rational number.

Every rational number does.

No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.

Related questions

The additive inverse of EVERY positive rational number is a negative number.

Yes.

The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.

It is a fundamental requirement of algebraic structures called groups.

For every number, a,there exists a number called the additive inverse, -a, such that a + -a = 0.

By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0Then p/q + (-p/q) = [p + (-p)] /q = 0/q.Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.

The additive inverse states that a number added to its opposite will equal zero. A + (-A) = 0. The "opposite" number here is the "negative" of the number. For any number n, the additive inverse is (-1)n. So therefore yes.

Yes. Just put a minus sign in front of it. Note that except for the zero, the additive inverse is no longer a natural number.

Yes.

One example would be a Galois Field size 4 (ie GF(4)). Here, the elements are {0,1,2,3} and every element is its own additive inverse.

To form the additive inverse, negate all parts of the complex number → 8 + 3i → -8 - 3i The sum of a number and its additive inverse is 0: (8 + 3i) + (-8 - 3i) = (8 + -8) + (3 + -3)i = (8 - 8) + (3 - 3)i = 0 + 0i = 0.

It is a tautological description of one of the basic properties of numbers used in the branch of mathematics called Analysis: Property 2: there exists an additive identity, called 0; for every number n: n + 0 = 0 + n = n. Property 3: there exists an additive inverse, of every number n denoted by (-n) such that n + (-n) = (-n) + n = 0 (the additive identity).